WASHINGTON—The Obama administration's proposal for forcing power plants to cut carbon emissions, due out Monday, is already becoming an explosive point of debate in some Senate and House midterm races that could prove treacherous for Democrats in energy-producing states.

The proposed rule, to be unveiled Monday by the Environmental Protection Agency, will kick off one of the largest political battles since the rollout last year of the Affordable Care Act. The rule will affect hundreds of fossil-fuel power plants and is destined to trigger lawsuits from states and industry, as well as attempts by Republicans and other opponents to craft a legislative response.

For President Barack Obama, the rule is the centerpiece of efforts to combat global warming and a major element of his attempt to secure a second-term legacy. While the president is expected to remain out of the spotlight when the EPA unveils the rule Monday, he plans to join a conference call with the American Lung Association, casting the rule as needed to protect public health as well as to reduce the carbon emissions that scientists say contribute to climate change.

But the rule has splintered Mr. Obama's own party and could weaken his political hand in his last two years in office by giving new ammunition to Republicans, who have a strong chance of stripping Democrats of their majority in the Senate.

Rep. Nick Rahall (D., W.Va.), who is among the most vulnerable House Democrats seeking re-election, said the rule's impact on coal-state Democrats is simply not the top priority at the White House.

"I'm sure that's not No. 1 in their minds. Probably, the president's legacy is No. 1," said Mr. Rahall, who opposes additional restrictions on coal plants.

The Republican message on the proposed rule is largely consistent across the country—an assertion that Democrats will raise energy costs and kill jobs, and that carbon restrictions are futile in the absence of similar action by China and other large polluting nations. Many Republicans are linking the rule to other Obama administration actions that they view as overly intrusive in the economy.

While Democrats are more vocal than Republicans in saying that man-made climate change is a problem, candidates in some energy-producing states are wary of backing a government response. Democrats Natalie Tennant in West Virginia and Alison Lundergan Grimes in Kentucky, both Senate candidates, oppose the rule, and both plan to spend the week showing their support for coal jobs.

"I will fight President Obama and anyone else who tries to undermine our coal jobs," Ms. Tennant said in a statement.

Ms. Tennant doesn't dispute the science of climate change, but she says the federal government should allow more time to develop affordable new coal-production technology before the administration proposes new rules. She plans to be at a coal-mining-training facility in Sophia, W.Va., on Tuesday to highlight her pro-coal stance.

But National Democrats without an allegiance to coal states say the EPA proposal could energize base voters—in particular young people who tend to vote in lesser numbers during midterm elections, and some of the party's top donors, such as billionaire environmentalist Tom Steyer, who is backing Democratic Senate candidates in many states.

"It's not going to be helpful in Kentucky or West Virginia," Rep. John Yarmuth (D., Ky.) said. "In terms of being able to do something to energize young people [in other states], this has the potential to do that for our side."

Other Democrats note that the president already is particularly unpopular in Kentucky and West Virginia, so allowing candidates in those states to show their independence may bolster them politically.

In fact, Ms. Grimes's campaign said the Democrat will try to link her opponent, Senate Minority Leader Mitch McConnell (R., Ky.), to the president, saying the longtime lawmaker is responsible for a decline in coal-industry jobs because he has failed to stop the federal government from its "war on coal."

Mr. McConnell will try to rebut Ms. Grimes's line of attack by introducing legislation this week that would block the proposed rule from being implemented. That effort stands virtually no chance of advancing in the Democratic-controlled Senate.

Mr. McConnell also will try to link his opponent to Mr. Obama. "Actions speak louder than words, and it is clear that Alison stands behind Barack Obama, Harry Reid and the war on coal they are waging," said Allison Moore, Mr. McConnell's spokeswoman.

Similarly, Ms. Tennant's opponent in the West Virginia Senate race, Rep. Shelley Moore Capito, has already criticized the expected rule in a letter sent Thursday to Mr. Obama.

One Democrat taking a different approach is Sen. Kay Hagan, who praised the EPA during a speech to local environmental activists last week, saying the agency's "ability to responsibly regulate greenhouse gas emissions is key to protecting our environment." Her calculus is that voters will welcome an environmental push after coal ash spilled into the state's Dan River in February.

Still, Ms. Hagan, who is in a tough race against North Carolina Republican state House speaker Thom Tillis, hasn't embraced the rule outright. She has asked the administration to extend the amount of time available for public comment.

Republicans there are already attacking Ms. Hagan, saying she is out to please her party's base. "The average voter that will decide these Senate races is more concerned about their jobs," said Rep. Patrick McHenry.